Our observations suggest that stripe and interstripe cells occupy distinct regions in ABM [1]} patterns. In comparison, the CA [2]} frequently produces outlier cells, such as an isolated black cell in the center of a gold interstripe; see Figure REF . Because the way that we compute persistent homology in Step 3 is sensitive to outliers like these [3]}, [4]}, we perform an initial cleaning step to remove stray cells. Focusing on the three cell types—\(M\) , \(X^\text{d}\) , and \(X^\ell \) —for which we compute persistent homology, we identify outliers by first finding the \(N_{nn}=10\)  nearest neighbors of each cell under the Euclidean norm on a domain that is periodic in \(x\) . We only consider neighbors of the same cell type, and we exclude each cell from counting itself. Using the distances \(\lbrace d_i\rbrace _{i=1,...,N_{nn}}\)  from the \(j\) th cell of type \(c \in \lbrace M, X^\text{d}, X^\ell \rbrace \)  to its nearest neighbors of type \(c\) , we compute \(D^c_j = \sqrt{\sum _{i=1}^{N_{nn}} d_i^2/N_{nn}}\) . If \(D^c_j \ge \theta ^c_m\) , where \(m \in \lbrace \text{ABM}, \text{CA}\rbrace \) , then we classify the \(j\) th cell of type \(c\)  as an outlier and remove it. This captures that outliers are in low-density areas, so their distance from their ten nearest neighbors is comparatively large.
